With no access to the Pacific but a new land border to the west, would the US military be larger or smaller than OTL?
You have decreed that US-British relations are friendly. I am dubious about this, as Britain boxing the US in on two sides, blocking any path to expansion and having the ability to cut off US access to the Mississippi (and by extension, sea access for most of the country west of the Appalachians) whenever it likes would, at least initially, make the US feel vulnerable and expand and exacerbate its OTL 19th century tendencies towards wanting to annex Canada. If relations are actually friendly, the military will be smaller, although initially it'll be of similar size to OTL. If relations are at times tense but never actually lead to (major) war, the military will be larger in the 19th century (due to the need to guard the Mississippi frontier from perfidious Albion) but probably still smaller in the long run due to the US being a somewhat smaller and weaker country on the whole.
What effect would this have on slavery? Could there still be a civil war?
If Britain abolishes it on schedule, the Underground Railroad will be able to route west instead of north. A slave in a plantation on the Mississippi doesn't need to flee to Canada: if they can just get across the river, they're free. This will exacerbate tensions between the US and the UK and could be the flash point for a war, but the scenario says they are friendly, so I guess either they work something out or the South just has to grin and bear it. The South having to grin and bear it could, of course, itself kick off a Civil War, as they rebel against the government after it refuses to press Britain on the issue. We also won't see a Missouri compromise. Without territory west of the Mississippi, balancing free and slave states becomes difficult: this might encourage the south to turn an eye towards Louisiana, or perhaps the Caribbean. Maine will probably stay part of Massachusetts for longer.
How would this affect the development of American cities? I assume that Chicago in TTL would be far less significant than in OTL.
It depends on how what would've been the Western US develops, but as a key link between the Great Lakes and the Mississippi, it will still be of great significance. It might not be the Second City ITTL, but even if it isn't it'll be one of the most populous and important in the Union. Cities along the Mississippi will be larger and more prosperous than IOTL due to their importance to the border trade.
How would this impact immigration? Is it possible for the US of TTL to attain the same population as the US of OTL, or would the population be much smaller?
Homesteaders who would've gone to Kansas or Oregon will still go to those places: they just won't be under US control. Unless you anticipate much higher immigration to/population growth in TTL's US than IOTL, and I don't see why you would, you'll wind up with a less populous country than OTL, although possibly one with more people than the region has IOTL due to immigration restrictions and/or language barriers discouraging people from migrating to the western portions of the sunbelt or whatever.
How would this affect America's position on the world stage? Assuming it still develops into an industrialized great power, would it try to project its influence across the globe or would it remain isolationist?
Diminished to no ability to project force into the Pacific, so probably no Hawaii or Philippines. It'll still be meddling in the Caribbean and Central America, though. Isolationism or interventionism will depend on how exactly the timeline proceeds: both are possible.
